If something akin to the Renaissance happens, ITTL it's probably as likely to originate in the Muslim lands as in the West. No Mongols means the great library of Baghdad is not destroyed; even if Mesopotamia was in relative decline in the 13th century, if those resources still exist it's more likely someone will make use of them eventually.
Not sure if it can't be both. A reflowering of Islam's Golden Age and a European Renaissance...
So much potential awesome art and science.